There are two questions here:
a two-day programme
a three-man committee
the use of the indefinite article refers to the words 'programme' and 'committee' which are singular, and thus allow (or sometimes require) the use of the indefinite article. Articles (and other determiners) are positioned at the beginning of a noun phrase, even though they refer to the head noun and not the words that directly follow them.
This is simply a way to construct this type of words (which are, as StoneyB pointed out, used for measurements). When you combine a number and a noun in this particular way you don't have two words any more, you have a new, compound word, which follows new rules. Compound words can be written unseparated (a bookworm, lifetime), with a hyphen (last-minute, sun-dried, two-day, three-man, etc.) or they can be written separately (world famous). With the type of compound words you are asking about, a hyphen is used.
Note that you would say:
I attended a two-day conference.
Which means that you attended a conference which lasted two days.
If you said:
I attended two days of the conference.
means that you were there for two days, but the conference may have (and probably has) lasted longer.
Or consider this example:
A two-word phrase is one that consists of two words.